Python 带GEKKO的MPC中的变量界

我正在尝试使用MPC和GEKKO实现恒温器控制

状态变量（温度）应在以下代码中预先规定的较低和较高温度值、

temp\u low

和

temp\u upper

范围内

这两个界限在一天中都不同：每小时一个值

目标函数是使用供暖的成本。价格也会随着一天的变化而变化，

TOU

如下

T_external

是在微分方程中起作用的房间外部温度

如何实现这一点以使其优化？

这是我的尝试：

from gekko import GEKKO
import numpy as np

m = GEKKO(remote=False)
m.time = np.linspace(0,23,24)

#initialize variables
T_external = [50.,50.,50.,50.,45.,45.,45.,60.,60.,63.,64.,45.,45.,50.,52.,53.,53.,54.,54.,53.,52.,51.,50.,45.]
temp_low = [55.,55.,55.,55.,55.,55.,55.,68.,68.,68.,68.,55.,55.,68.,68.,68.,68.,55.,55.,55.,55.,55.,55.,55.]
temp_upper = [75.,75.,75.,75.,75.,75.,75.,70.,70.,70.,70.,75.,75.,70.,70.,70.,70.,75.,75.,75.,75.,75.,75.,75.]
TOU = [0.05,0.05,0.05,0.05,0.05,0.05,0.05,200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,0.05,0.05,0.05]

b = m.Param(value=1.)
k = m.Param(value=0.05)
T_e = m.Param(value=T_external)

u = m.MV(value=[0]*24, lb=[0.0]*24, ub=[1.]*24)
u.STATUS = 1  # allow optimizer to change

# Controlled Variable
T = m.SV(value=[60]*24, lb=temp_low, ub=temp_upper)

m.Equation(T.dt() == k*(T_e-T) + b*u)

m.Obj(np.dot(TOU,u))

m.options.IMODE = 6
m.solve(debug=True)

当我运行此命令时，我得到：

@error: Model Expression
 *** Error in syntax of function string: Missing operator

Position: 4                   
 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
    ?

---

Gekko需要常量作为不等式表达式，其中变量

T

与上

TH

或下

TL

值进行比较。如果您有

b=1。

，则会导致不可行的解决方案，因为加热器功率不足，无法将温度维持在上限和下限范围内。我将值更改为

b=10

，以获得可行的解决方案

从gekko导入gekko
将numpy作为np导入
m=GEKKO（远程=False）
m、 时间=np.linspace（0,23,24）
#初始化变量
T_external=[50,50,50,50,45,45,60,60,63,\
64.,45.,45.,50.,52.,53.,53.,54.,54.,\
53.,52.,51.,50.,45.]
温度低=[55,55,55,55,55,55,55,55,55,68,68,68,68,\
55.,55.,68.,68.,68.,68.,55.,55.,55.,55.,55.,55.,55.]
温度上限=[75,75,75,75,75,75,75,75,70,70,70,70,75,\
75.,70.,70.,70.,70.,75.,75.,75.,75.,75.,75.,75.]
TOU_v=[0.05,0.05,0.05,0.05,0.05,0.05,0.05200,200,200,200,200,\
200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,0.05,\
0.05,0.05]
b=m.Param（值=10.）
k=m.Param（值=0.05）
T_e=m.Param（值=T_外部）
TL=m.Param（值=温度低）
TH=m.Param（值=温度上限）
TOU=m.Param（值=TOU_v）
u=m.MV（磅=0，磅=1）
u、 状态=1#允许优化器更改
#受控变量
T=m.SV（值=60）
m、 方程式([T>=TL，T非常感谢您的帮助，这真是令人印象深刻。有一件事让我很感兴趣。昨天我一直试图让它工作，最后我用
IMODE=3
和
b=1.0
完成了。有什么不同，在一种模式下它工作，而在另一种模式下它导致不可行的解决方案。我在这里发布了一个问题：.Kind regards.我很乐意为这篇文章添加一个更详细的回复。
IMODE=3
将所有导数值设置为零，但您在另一种模式下的解决方案也允许初始条件更改为更高的值，这样加热器就不需要强大才能保持可行性。我如何在目标函数中编写这样的软约束n我想记录我的算法。？我是否只需在目标函数中添加e_{H}*权重和e_{L}*权重？@John Hedengren。以下是关于具有l1范数目标的CV目标函数的更多信息：